A tank contains 180 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

Step-by-step explanation:

Given that:

A tank contains 180 liters of fluid in which 50 grams dissolved inside.

Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 6 L/min

The salt pumped out of initial amount added salt

At (t = 0) = 50

To determine the number A (t)

Integrating factor  

Taking integral on the both sides;

At  A(t = 0) = 50

50 = 180  + C            (assuming C = )

C = 50 - 180

C = 130